The Stanford Encyclopedia of Philosophy has added a brand new entry, The Problem of Induction. John Vicker's survey of the promise and peril of inductive reasoning necessarily gets into logic - I'm bad at it - but it's ultimately connected to our ideas about infinity, which, as Cambridge cosmologist John Barrow said at the ideaFestival in October can now be mathematically approached, as well as Kurt Gödel's incompleteness theorems (he unfortunately could not attend), who demonstrated that whole systems are never entirely logical, and logical systems are never complete.
In an infinite universe the data set is always in progress.
So if inductive conclusions cannot be justified, why trust induction at all? Because it can be self correcting. Though ultimately - and infinitely - self-referential, it excels as a method for prediction, and coupled with the imagination is a kind of future reasoning.
So yes, the bias is built in. And from that bias, knowledge grows.